Analyticity of quantum states in one-dimensional tight-binding model
Analyticity of quantum states in one-dimensional tight-binding model
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DOI：
10.1140/epjb/e2014-50210-6
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
H. Yamada;K. Ikeda
中科院分区：
文献类型：
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作者：
H. Yamada;K. Ikeda
量子波函数的复解析复杂性（其辐角扩展到复平面）提供了一个重要的信息，可以用来描述复杂的量子动力学，如时间不可逆性、耗散性等.本文利用Pade近似和一些补充方法研究了杂质态、Anderson定域态和哈珀模型定域态等量子态的复解析性质.杂质态可以用Pade近似的简单极点来表征，而安德森模型和哈珀模型的局域态可以用Pade近似函数沿着一个临界边界的极点和零点的累积来表征，临界边界隐含着一个自然边界（NB）.采用基于移动展开中心的互补方法，数值证实了NB的存在，并强烈地表明在复延拓中，哈珀模型的Anderson定域态和定域态都存在NB.此外，我们讨论了一个有趣的关系，我们的研究和自然边界问题的潜在功能的密切联系的本地化问题是最近发现的一些数学家。此外，我们研究的有用性的Pade近似数值预测NB的存在通过两个典型的例子，缺项幂级数和随机幂级数。
Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and so on. We examine Pade approximation and some complementary methods to investigate the complex-analytical properties of some quantum states such as impurity states, Anderson-localized states and localized states of Harper model. The impurity states can be characterized by simple poles of the Pade approximation, and the localized states of Anderson model and Harper model can be characterized by an accumulation of poles and zeros of the Pade approximated function along a critical border, which implies a natural boundary (NB). A complementary method based on shifting the expansion-center is used to confirm the existence of the NB numerically, and it is strongly suggested that the both Anderson-localized state and localized states of Harper model have NBs in the complex extension. Moreover, we discuss an interesting relationship between our research and the natural boundary problem of the potential function whose close connection to the localization problem was discovered quite recently by some mathematicians. In addition, we examine the usefulness of the Pade approximation for numerically predicting the existence of NB by means of two typical examples, lacunary power series and random power series.